Question

Solve the following system of linear equations. -3 x -y = 7 and 6x+7y = 11

a) x = -2, y = 1
b) x = 3, y = -2
c) x = -1, y = 2
d) x = 2, y = -1

Answer 1

To solve the given system of linear equations, -3x - y = 7 and 6x + 7y = 11, we use the elimination method. After elimination and substitution, we find x = 38 and y = -31, which do not match any of the provided answer choices, suggesting an error in the question or choices.

Step-by-step explanation:

To solve the system of linear equations given by -3x - y = 7 and 6x + 7y = 11, we can use the method of substitution or elimination. In this scenario, we will use the elimination method for a clearer solution.

1. First, we will try to eliminate one variable by making the coefficients of either x or y the same. Multiplying the first equation by 6 gives us -18x - 6y = 42.
2. Now we have two equations, -18x - 6y = 42 and 6x + 7y = 11. Adding these equations together cancels out x, leaving us with y = -31.
3. Substitute y = -31 into one of the original equations to find x. We'll use the second equation: 6x + 7(-31) = 11, which simplifies to 6x - 217 = 11. Solving for x gives us x = 38.

The solution to the system of equations is x = 38 and y = -31. However, none of the provided answer choices match this solution, indicating there might have been an error in either the question or the provided choices.